### Primary Contributors:
Philip Beeley and † Christoph J. Scriba (1929–2013)

Philip Beeley and † Christoph J. Scriba (1929–2013)

### John Wallis (1616–1703)

John Wallis, the Savilian professor of geometry in Oxford from 1649 until his death 54 years later, is renowned today as one of the leading mathematicians of the seventeenth century. Yet in a manner characteristic of the time, his interest and accomplishments spread far wider.

He acted as secretary to the reforming Assembly of Divines in the 1640s, acquired fame as a brilliant cryptanalyst during the civil wars, was a leading member of the natural philosophical circle in Oxford during the Commonwealth and the Royal Society at the Restoration, and — controversially — held the post of keeper of the university archives jointly with his mathematical chair. Alongside important mathematical works, his publications include major treatises on ancient and modern music theory, a pioneering grammar of the English language, and the foremost survey of logic produced in Britain during his lifetime.

#### Partners and Additional Contributors

Metadata for the Wallis records featured currently in EMLO was contributed by Dr Philip Beeley and it was calendared for upload during the first phase of Cultures of Knowledge by Dr Kim McLean-Fiander. Cultures of Knowledge and Philip Beeley would like to thank Sue Burgess for her help with the ingestion of this metadata into EMLO.

#### Key Bibliographic Source(s)

*The Correspondence of John Wallis (1616–1703),* Volume 1 (1641–1659), ed. Philip Beeley and Christoph J. Scriba (Oxford: OUP, 2003).

*The Correspondence of John Wallis (1616–1703),* Volume 2 (1660–September 1668), ed. Philip Beeley and Christoph J. Scriba (Oxford: OUP, 2005).

*The Correspondence of John Wallis (1616–1703), *Volume 3 (October 1668–1671), ed. Philip Beeley and Christoph J. Scriba (Oxford: OUP, 2012).

*The Correspondence of John Wallis (1616–1703)*, Volume 4 (1672–April 1675), ed. Philip Beeley and Christoph J. Scriba (Oxford: OUP, 2014).

#### Contents

Wallis’s correspondence was equally wide-ranging geographically and thematically: he engaged in public dispute with a range of figures including Hobbes, Holder, Fermat, and Roberval, and corresponded with leading scientific luminaries such as Boyle, Newton, Leibniz, Huygens, and Flamsteed, as well as scientific amateurs, theologians, and members of government. His roughly 2,000 extant letters, exchanged with astronomers, mathematicians, philosophers, and linguists throughout Europe, document his role not only as a key figure in the international Republic of Letters itself, but also in establishing Oxford as an important hub within that broader network after a period in which it had been marginal to European intellectual affairs. Wallis represents, therefore, a contrasting institutional setting which gave rise to cultures of knowledge instructively different to those fostered by the networks of John Aubrey, Samuel Hartlib, or Jan Amos Comenius. Wallis’s correspondence provides a crucial link between the earliest English correspondence network surrounding the Prussian-born intelligencer Hartlib and the domestication of this kind of networking activity by the era of Aubrey.

### Provenance

Wallis regarded scientific correspondence as an important record of intellectual developments, and in consequence published some of his own letters during his lifetime. More recently, a number have been published in modern editions of the letters of his most important scientific contemporaries. Yet the overwhelming majority of his letters remain in manuscript and are virtually unstudied. The Bodleian Library contains the largest manuscript holdings of Wallis’s communications as well a huge range of related material, including his lecture notes from the 1650s, drafts of numerous publications, originals and copies of many of the papers which he deciphered from the 1640s onwards, and notes on books by other authors, as well as his marginalia in books which were or became part of the Savilian Library itself. Hundreds of additional letters, the existence of which has gone unnoticed hitherto, have been discovered recently in the University Archives, throwing fresh light on academic life and university politics throughout Wallis’s Oxford career. In response to this situation, Philip Beeley and the late Christoph Scriba have published four of the proposed eight volumes of the scholarly edition of Wallis’s correspondence. These four volumes appeared with OUP in 2003, 2005, 2012, and 2014.

#### Further resources

**Bibliography**

**Primary Editions
**

*The Correspondence of John Wallis (1616–1703)*, eds. Philip Beeley and Christoph J. Scriba, 4 vols to date of 8 vols planned (Oxford: Oxford University Press, 2003–).

Wallis, John, *Opera mathematica*, 3 vols, Oxford 1693–1699; repr. with foreword by Christoph J. Scriba (Hildesheim and New York: Georg Olms, 1972).

— , The Arithmetic of Infinitesimals, tr. and intr. Jacqueline A. Stedall (New York, Berlin, and Heidelberg: Springer, 2004).

Secondary Works

Beeley, Philip, ‘Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics’, in Ursula Goldenbaum and Douglas M. Jesseph, eds, *Infinitesimal Difference: Controversies between Leibniz and his Contemporaries* (Berlin and New York: De Gruyter, 2008), pp. 31–52.

— , and Scriba, Christoph J. , ‘Disputed Glory. John Wallis and Some Questions of Precedence in Seventeenth-Century Mathematics’, in Hartmut Hecht, Regina Mikosch, et al., eds, *Kosmos und Zahl. Beiträge zur Mathematik- und Astronomiegeschichte, zu Alexander von Humboldt und Leibniz* (Stuttgart: Franz Steiner, 2008), pp. 275–99.

— , and Scriba, Christoph J. , ‘Controversy and Modernity. John Wallis and the Seventeenth-Century Debate on the Nature of the Angle of Contact’, *Acta Historica Leopoldina*, 54 (2008), pp. 431–50.

— , ‘Eine Geschichte zweier Städte. Wallis, Wilkins und der Streit um die wahren Ursprünge der Royal Society’, *Acta Historica Leopoldina*, 49 (2008), pp. 135–62.

— , ‘Un de mes amis. On Leibniz’s Relation to the English Mathematician and Theologian John Wallis’, in Pauline Phemister and Stuart Brown, eds, *Leibniz and the English-Speaking World* (Dordrecht: Springer, 2007), pp. 63–81.

— , and Scriba, Christoph J. , ‘Wallis, Leibniz und der Fall von Harriot und Descartes. Zur Geschichte eines vermeintlichen Plagiats im 17. Jahrhundert’, *Acta Historica Leopoldina*, 45 (2005), pp. 115–29.

— , and Probst, Siegmund, ‘John Wallis (1616-1703): Mathematician and Divine’, in L. Bergmans and Teun Koetsier, eds, *Mathematics and the Divine* (Amsterdam: Elsevier, 2005), pp. 441–57.

Freudenthal, Gideon, ‘A Rational Controversy over Compounding Forces’, in Peter Machamer, Marcello Pera and Aristides Baltas, eds, *Scientific Controversies: Philosophical and Historical Perspectives* (New York and Oxford: Oxford University Press, 2000), pp. 125–42.

Jesseph, Douglas M., *Squaring the Circle: The War between Hobbes and Wallis* (Chicago and London: University of Chicago Press, 1999).

Malet, Antoni, ‘Barrow, Wallis, and the Remaking of Seventeenth-Century Indivisibles’, *Centaurus*, 39 (1997), pp. 67–92.

Mancosu, Paolo, *Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century* (Oxford and New York: Oxford University Press, 1996).

Maierù, Luigi, *John Wallis. Una vita per un progetto* (Soveria Mannelli: Rubbettino, 2007).

Probst, Siegmund, ‘Infinity and Creation: The Origin of the Controversy between Thomas Hobbes and the Savilian Professors Seth Ward and John Wallis’, *British Journal of the History of Science*, 26 (1993), pp. 271–79.

— , *Die mathematische Kontroverse zwischen Thomas Hobbes und John Wallis* (Hanover: Private Imprint, 1997/University of Regensburg: PhD thesis, 1994).

Prytz, Johan, *A Study of the Angle of Contact with a Special Focus on John Wallis’ Conception of Quantities and Angles* (University of Uppsala: PhD thesis, 1994).

Pycior, Helena, ‘Mathematics and Philosophy: Wallis, Hobbes, Barrow, and Berkeley’, *Journal of the History of Ideas*, 48 (1987), pp. 265–86.

Rampelt, Jason, ‘The Last Word: John Wallis on the Origin of the Royal Society’, *History of Science*, 46 (2008), pp. 177–201.

— , *Distinctions of Reason and Reasonable Distinctions: The Academic Life of John Wallis (1616–1703)* (University of Cambridge: PhD thesis, 2005).

Scott, Joseph Frederick, T*he Mathematical Work of John Wallis, D.D., F.R.S. (1616–1703)* (London, 1938; repr. New York: Chelsea, 1981).

Scriba, Christoph. J., ‘The Autobiography of John Wallis, F.R.S.’, *Notes and Records of the Royal Society of London*, 25 (1970), pp. 17–46.

— , *Studien zur Mathematik des John Wallis (1616–1703)* (Wiesbaden: Franz Steiner, 1966).

Stedall, Jacqueline A., *A Discourse Concerning Algebra: English Algebra to 1685* (Oxford and New York: Oxford University Press, 2002).

— , ‘Of our own nation: John Wallis’s Account of Mathematical Learning in Medieval England’, *Historia Mathematica*, 28 (2001), pp. 73–122.